We look at the division of 102561 by 83 
We want to figure out the number of times 102561 can be divided by 83.

On to step 1:
When dividing 1 by 83, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 83

Let's proceed to step 2:
The number 83 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 83

Step 3:
102 divided by 83 is 1 with a remainder of 19.
The next digit of our result is 1. 
Result so far: 1.0
If we take 83 away from 102, we end up with 19.
Take the next digit (5) from the dividend and append it to 19, then repeat: 195 / 83

Advancing to step 4:
195 divided by 83 is 2 with a remainder of 29.
Put 2 as the next digit of the answer. 
Result so far: 12.0
If we take 166 away from 195, we end up with 29.
Grab the next digit (6) from the dividend, add it to 29, then carry on: 296 / 83

Step 5:
When dividing 296 by 83, we get 3 with a remainder of 47.
Write down 3 as next digit of the result. 
Result so far: 123.0
If we take 249 away from 296, we end up with 47.
Append the next digit (1) from the dividend to 47 and continue with: 471 / 83

Advancing to step 6:
471 divided by 83 is 5 with a remainder of 56.
Write down 5 as next digit of the result. 
Result so far: 1235.0
Subtracting 415 from 471 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Moving on to step 7:
When dividing 560 by 83, we get 6 with a remainder of 62.
Put 6 as the next digit of the answer. 
Result so far: 1235.6
Deduct 498 from 560 and we're left with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Step 8:
The number 83 fits into 620 7 times, leaving a remainder of 39.
Put 7 as the next digit of the answer. 
Result so far: 1235.67
The remainder is 39 after subtracting 581 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Step 9:
83 goes into 390 4 times with a remainder of 58.
Record the quotient 4 as the next digit in the result. 
Result so far: 1235.674
The remainder is 58 after subtracting 332 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 10:
The number 83 fits into 580 6 times, leaving a remainder of 82.
Write down 6 as next digit of the result. 
Result so far: 1235.6746
The remainder is 82 after subtracting 498 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Going ahead to step 11:
83 goes into 820 9 times with a remainder of 73.
Write down 9 as next digit of the result. 
Result so far: 1235.67469
If we subtract 747 from 820, we get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Let's proceed to step 12:
83 can be fit into 730 8 times, resulting in a remainder of 66.
The next digit of our result is 8. 
Result so far: 1235.674698
Subtracting 664 from 730 leaves us with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Going ahead to step 13:
83 goes into 660 7 times with a remainder of 79.
Use 7 as the next digit of our solution. 
Result so far: 1235.6746987
If we subtract 581 from 660, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Let's proceed to step 14:
When dividing 790 by 83, we get 9 with a remainder of 43.
Record the quotient 9 as the next digit in the result. 
Result so far: 1235.67469879
The remainder is 43 after subtracting 747 from 790.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

After the division, we end up with 1235.67469879 and a remainder of 4.3e-08.